CN115077561B - Method and system for adaptively compensating damping anisotropy of hemispherical harmonic oscillator - Google Patents
Method and system for adaptively compensating damping anisotropy of hemispherical harmonic oscillator Download PDFInfo
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Abstract
The invention provides a method and a system for adaptively compensating the damping anisotropy of a hemispherical harmonic oscillator, which comprises the following steps: obtaining a motion equation of the hemispherical harmonic oscillator; based on the motion equation, applying energy control, orthogonal control, initial self-precession control and phase control to the hemispherical harmonic oscillator to obtain a stable working state of the hemispherical harmonic oscillator; performing partial differential operation on the energy control based on the stable working state, and overlapping the energy control with the initial automatic precession control to obtain final automatic precession control; and eliminating the damping anisotropy of the hemispherical harmonic oscillator based on the final automatic precession control. The invention has the advantages of applicability to most of full-angle mode vibration gyros, good compensation effect and strong reliability.
Description
Technical Field
The invention belongs to the technical field of intelligent instruments and meters, and particularly relates to a method and a system for adaptively compensating the anisotropic damping of a hemispherical harmonic oscillator.
Background
A hemispherical resonator gyroscope is a vibrating gyroscope based on the coriolis effect. When no external angular velocity is input, the vibration mode of the standing wave is fixed at a certain position of the hemispherical harmonic oscillator. When an external angular velocity is input, the coriolis force causes the relative displacement between the standing wave mode and the hemispherical resonator, and the ratio of the relative rotational angular velocity to the external input angular velocity is a constant value, which is called a precession factor. In the actual working process of the hemispherical resonator gyroscope, firstly, a displacement signal of a sensitive vibration mode is sensed, then the displacement signal is converted into a voltage signal, then, a standing wave rotation angle is obtained through further calculation, the rotation angular speed of the hemispherical resonator gyroscope is calculated by combining with a precession factor, and finally, the measurement requirement is finished.
Due to the limitation of the processing technology, the hemispherical harmonic oscillator generally has the conditions of surface cracks, uneven metal coating, uneven circumferential mass distribution and the like, and is mainly represented by rigidity anisotropy and damping anisotropy. The rigidity anisotropy can be solved through frequency modulation and orthogonal control, the existence of the damping anisotropy can cause the gyroscope to generate an angle self-locking effect under the condition of low rotating speed input, and an angle drift error still exists under the condition of high rotating speed input. At present, an effective means for compensating the damping anisotropy of the hemispherical harmonic oscillator is not available. Therefore, the invention provides a method and a system which are convenient to implement and can self-adaptively compensate the damping anisotropy of the hemispherical harmonic oscillator.
Disclosure of Invention
In order to solve the technical problems, the invention provides a method and a system for adaptively compensating the damping anisotropy of a hemispherical harmonic oscillator, which have the advantages of applicability to most of full-angle mode vibration gyros, good compensation effect and strong reliability.
In order to achieve the above object, the present invention provides a method for adaptively compensating the damping anisotropy of a hemispherical resonator, comprising the following steps:
obtaining a motion equation of the hemispherical harmonic oscillator;
based on the motion equation, applying energy control, orthogonal control, initial self-precession control and phase control to the hemispherical harmonic oscillator to obtain a stable working state of the hemispherical harmonic oscillator;
performing partial differential operation on the energy control based on the stable working state, and overlapping the energy control with the initial automatic precession control to obtain final automatic precession control;
and eliminating the damping anisotropy of the hemispherical harmonic oscillator based on the final self-precession control.
Optionally, the equation of motion is:
wherein E represents an energy signal, Q represents a quadrature signal,
representing damping anisotropy, theta τ Representing the damping misalignment angle, Δ ω representing the stiffness anisotropy, θ ω Representing a stiffness misalignment angle, omega representing an ambient input angular velocity, theta representing a gyro precession angle, gamma representing a gyro precession factor, delta representing a phase difference between a gyro vibration signal and a reference signal,
which represents the differential of the energy signal and,
is the differential of the quadrature signal and is,
is the differential of the precession angle of the gyroscope,
is the differential of the phase difference between the gyro vibration signal and the reference signal.
Optionally, the final auto-precession control f qs The calculation formula of (c) is:
wherein, f qs0 For initial self-precession control, f as For energy control, ω represents the average resonance frequency of the hemispherical harmonic oscillator.
Optionally, based on the final self-precession control, a method of eliminating the damping anisotropy of the hemispherical resonator is:
and applying the final self-precession control to a differential equation of a gyro precession angle to obtain a variation relation between an angle signal and an external input angular velocity, and eliminating the damping anisotropy of the hemispherical harmonic oscillator.
Optionally, the calculation formula of the variation relationship between the angle signal and the external input angular velocity is:
in another aspect, to achieve the above object, the present invention provides a system for adaptively compensating damping anisotropy of a hemispherical resonator, including: the device comprises a first obtaining module, a second obtaining module, a third obtaining module and a eliminating module;
the first obtaining module is used for obtaining a motion equation of the hemispherical harmonic oscillator;
the second obtaining module is used for applying energy control, orthogonal control, initial self-precession control and phase control to the hemispherical harmonic oscillator based on the motion equation to obtain a stable working state of the hemispherical harmonic oscillator;
the third obtaining module is used for performing partial differential operation on the energy control based on the stable working state, and overlapping the energy control with the initial automatic precession control to obtain final automatic precession control;
and the elimination module is used for eliminating the damping anisotropy of the hemispherical harmonic oscillator based on the final automatic precession control.
Optionally, the equation of motion is:
wherein E represents an energy signal, Q represents a quadrature signal,
representing damping anisotropy, theta τ Representing the damping misalignment angle, Δ ω representing the stiffness anisotropy, θ ω Representing a stiffness misalignment angle, omega representing an external input angular velocity, theta representing a gyro precession angle, gamma representing a gyro precession factor, and delta representing a difference between a gyro vibration signal and a reference signalThe phase difference between the two phases is small,
which represents the differential of the energy signal and,
is a differential of the quadrature signal and is,
is the differential of the precession angle of the gyroscope,
is the differential of the phase difference between the gyro vibration signal and the reference signal.
Optionally, the final auto-precession control f qs The calculation formula of (c) is:
wherein f is qs0 For initial self-precession control, f as For energy control, ω represents the average resonant frequency of the hemispherical harmonic oscillator.
Optionally, based on the final auto-precession control, a process of eliminating the damping anisotropy of the hemispherical resonator is:
and applying the final self-precession control to a differential equation of the gyro precession angle to obtain a variation relation between an angle signal and an external input angular speed, and eliminating the damping anisotropy of the hemispherical harmonic oscillator.
Optionally, the calculation formula of the variation relationship between the angle signal and the external input angular velocity is as follows:
compared with the prior art, the invention has the following advantages and technical effects:
1. the angle drift error caused by the damping anisotropy of the hemispherical harmonic oscillator can be compensated in a self-adaptive manner in a full-angle mode;
2. the method has good effect on the application scenes of high-rotating-speed input and low-rotating-speed input of the full-angle hemispherical resonant gyroscope;
3. the invention has the advantages of applicability to most of full-angle mode vibration gyros, good compensation effect and strong reliability.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, are included to provide a further understanding of the application, and the description of the exemplary embodiments of the application are intended to be illustrative of the application and are not intended to limit the application. In the drawings:
fig. 1 is a schematic flow chart of a method for adaptively compensating the anisotropy of damping of a hemispherical resonator according to an embodiment of the present invention;
fig. 2 is a signal processing block diagram of a method for adaptively compensating the damping anisotropy of a hemispherical resonator according to an embodiment of the present invention.
Detailed Description
It should be noted that, in the present application, the embodiments and features of the embodiments may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer-executable instructions and that, although a logical order is illustrated in the flowcharts, in some cases, the steps illustrated or described may be performed in an order different than presented herein.
Example one
As shown in fig. 1, the present invention provides a method for adaptively compensating the damping anisotropy of a hemispherical resonator, comprising the following steps:
step 1: when the nonideal hemispherical resonator gyroscope is in a normal working state, the nonideal hemispherical resonator moves under an elliptical coordinate system to obtain a motion equation;
further, the non-ideal hemisphere harmonic oscillator moves according to the following differential equation in an elliptical coordinate system:
wherein E represents an energy signal, Q represents a quadrature signal,
representing damping anisotropy, theta τ Representing the damping misalignment angle, Δ ω representing the stiffness anisotropy, θ ω Representing a stiffness misalignment angle, omega representing an ambient input angular velocity, theta representing a gyro precession angle, gamma representing a gyro precession factor, delta representing a phase difference between a gyro vibration signal and a reference signal,
which represents the differential of the energy signal and,
is the differential of the quadrature signal and is,
is the differential of the precession angle of the gyroscope,
is the differential of the phase difference between the gyro vibration signal and the reference signal.
And 2, step: applying energy control f to spinning top as Quadrature control f qc Initially self-advancingDynamic control f qs0 Phase control f ac ；
Further, in the full angle mode, the hemispherical resonator gyro is energized to control f as Quadrature control f qc Initial automatic precession control f qs0 Phase control f ac The nonideal hemisphere harmonic oscillator moves under an elliptic coordinate system according to the following differential equation:
when the gyroscope works stably, the vibration amplitude of the gyroscope is kept stable, namely the energy signal
Is 0 while the quadrature control ensures that the quadrature signal Q is 0, i.e.
And step 3: energy control f under the stable working state of the gyroscope as Performing partial differential operation, and f qs0 The final automatic precession control f is obtained by superposition qs ；
Further, when
When f is present as The relationship to the gyro energy signal E is:
further, the following are obtained:
to eliminate the effect of angular drift due to damping anisotropy, a cancellation formula is required
In (1)
Therefore, to make the self-precession control term and the damping error term cancel each other, the following terms:
in this case:
the formula shows that:
in the formula (I), the compound is shown in the specification,
the value of 0 cannot be obtained, and whether the full-angle hemispherical resonator gyroscope breaks through the self-locking effect cannot be determined under the condition that the external input angular speed is low, so that the method is not established or has large error under the condition of low rotating speed. Thus additional stacking of the initial f is required qs0 Make the hemispherical harmonic oscillator maintain a stable self-precession state, and then control energy f as Performing partial differential operation, and f qs0 Superimposed to obtain new f qs Finally, the elimination of the damping anisotropy, i.e. f qs Expressed as:
i.e. automatic precessional control f qs By initial self-precession control of f qs0 And energy control trimming term
Are combined together.
And 4, step 4: and eliminating the damping anisotropy of the hemispherical harmonic oscillator by utilizing self-precession control.
Further, applying an automatic precession control f to the spinning top qs Order:
the change of the angle signal theta is only related to omega and is related to
Irrelevant, it is shown that the effect of damping anisotropy is eliminated.
As shown in fig. 2: collecting two paths of signals of an X mode axis and a Y mode axis by a hemispherical harmonic oscillator detection electrode, demodulating the two paths of signals into c after analog-to-digital conversion and signal demodulation x 、s x 、c y 、s y Four kinds of signals; substituting the energy signal E, the orthogonal signal Q, the angle signal theta and the phase signal delta into an ellipse parameter resolving equation to obtain an energy signal E, an orthogonal signal Q, an angle signal theta and a phase signal delta respectively; the four signals are respectively led into an energy control f as Quadrature control f qc Self-precession control f qs Phase control f ac . The driving signal generating module is used for modulating and generating a driving signal for the driving electrode, the driving signal is sent to the driving electrode through digital-to-analog conversion to control the movement of the hemispherical harmonic oscillator, and the whole process is a self-adaptive compensation hemispherical harmonic oscillator damping anisotropy control resolving block diagram.
Furthermore, the effectiveness of the method for adaptively compensating the anisotropy of the hemispherical harmonic oscillator damping is verified by taking the compensation of the gyro drift caused by the anisotropy of the hemispherical harmonic oscillator damping as an embodiment.
The nonideal hemisphere harmonic oscillator moves under an elliptic coordinate system according to the following differential equation:
during the movement of the top, energy control f is applied to the top as Quadrature control f qc Phase control f ac Self-precession control f qs0 The hemispherical resonator gyroscope is made to work in a stable working state, at the moment
Controlling the energy f as Partial differentiation of precession angle theta into self-precession control f qs ：
At this time
The following steps are changed:
the result shows an angle signal
The change of the semi-spherical harmonic oscillator is in a linear relation with the external input angular velocity omega, so that the error caused by the anisotropic damping of the semi-spherical harmonic oscillator in the full-angle semi-spherical resonant gyroscope is eliminated, and the effectiveness of the semi-spherical harmonic oscillator is proved.
The invention also provides a system for adaptively compensating the anisotropic damping of the hemispherical harmonic oscillator, which comprises the following components: the device comprises a first obtaining module, a second obtaining module, a third obtaining module and a eliminating module;
the first obtaining module is used for obtaining a motion equation of the hemispherical harmonic oscillator;
the second obtaining module is used for applying energy control, orthogonal control, initial self-precession control and phase control to the hemispherical harmonic oscillator based on a motion equation to obtain a stable working state of the hemispherical harmonic oscillator;
the third obtaining module is used for performing partial differential operation on energy control based on the stable working state, and overlapping the partial differential operation with the initial automatic precession control to obtain final automatic precession control;
and the elimination module is used for eliminating the damping anisotropy of the hemispherical harmonic oscillator based on final self-precession control.
Further, the equation of motion is:
wherein E represents an energy signal, Q represents a quadrature signal,
representing damping anisotropy, theta τ Representing the damping misalignment angle, Δ ω representing the stiffness anisotropy, θ ω Representing the stiffness misalignment angle, omega representing the ambient input angular velocity, theta representing the gyro precession angle, gamma representing the gyro precession angleA motion factor, delta, representing the phase difference between the gyro vibration signal and the reference signal,
which represents the differential of the energy signal and,
is a differential of the quadrature signal and is,
is the differential of the precession angle of the gyroscope,
is the differential of the phase difference between the gyro vibration signal and the reference signal.
Further, final automatic precession control f qs The calculation formula of (c) is:
wherein f is qs0 For initial self-precession control, f as For energy control, ω represents the average resonant frequency of the hemispherical harmonic oscillator.
Further, based on the final self-precession control, the process of eliminating the damping anisotropy of the hemispherical harmonic oscillator is as follows:
and applying the final self-precession control to a differential equation of the gyro precession angle to obtain a change relation between an angle signal and an external input angular velocity, and eliminating the damping anisotropy of the hemispherical harmonic oscillator.
Further, the calculation formula of the variation relation between the angle signal and the external input angular velocity is as follows:
the above description is only for the preferred embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (4)
1. A method for adaptively compensating the damping anisotropy of a hemispherical harmonic oscillator is characterized by comprising the following steps of:
obtaining a motion equation of the hemispherical harmonic oscillator;
based on the motion equation, applying energy control, orthogonal control, initial self-precession control and phase control to the hemispherical harmonic oscillator to obtain a stable working state of the hemispherical harmonic oscillator;
in the full-angle mode, applying energy control f to the hemispherical resonator gyroscope as Quadrature control f qc Initial automatic precession control f qs0 Phase control f ac The nonideal hemisphere harmonic oscillator moves under an elliptic coordinate system according to the following differential equation:
wherein E represents an energy signal and E represents a power signal,
indicating the damping directionsOpposite, theta denotes the gyro precession angle, theta τ Representing the damping misalignment angle, ω represents the average resonant frequency of the hemispherical resonator,
for the differential of the quadrature signal, Δ ω represents the stiffness anisotropy, θ ω The angle of the stiffness misalignment is indicated,
is the differential of the gyro precession angle, gamma represents the gyro precession factor, omega represents the external input angular velocity, theta τ Representing the damping misalignment angle, delta representing the phase difference between the gyro vibration signal and the reference signal, tau representing the damping time constant, E representing the differential of the energy signal,
is a differential of the phase difference between the gyro vibration signal and the reference signal,
when the gyroscope works stably, the vibration amplitude is kept stable, and the energy signal is differentiated
Is 0 while the quadrature control ensures that the quadrature signal Q is 0, i.e.
Based on the stable working state, performing partial differential operation on the energy control, and superposing the energy control with the initial automatic precession control to obtain final automatic precession control;
when the temperature is higher than the set temperature
When f is turned on as The relationship to the gyro energy signal E is:
further obtaining:
eliminating type
In (1)
Item (1): making the self-precession control term and the damping error term offset with each other, and making:
this time is:
the formula shows that:
in the formula (I), the compound is shown in the specification,
cannot be 0;
additional superposition of the initial f qs0 Make the hemispherical harmonic oscillator maintain a stable self-precession state and control energy f as Performing partial differential operation, and f qs0 Superpose to obtain new f qs Finally, the elimination of the damping anisotropy is achieved, f qs Expressed as:
self-precession control f qs By initial self-precession control of f qs0 And energy control trimming term
The components are combined together;
eliminating the damping anisotropy of the hemispherical harmonic oscillator based on the final self-precession control;
based on the final automatic precession control, the method for eliminating the damping anisotropy of the hemispherical harmonic oscillator comprises the following steps:
applying the final self-precession control to a differential equation of a gyro precession angle to obtain a variation relation between an angle signal and an external input angular velocity, and eliminating damping anisotropy of the hemispherical harmonic oscillator;
the calculation formula of the change relation between the angle signal and the external input angular speed is as follows:
2. the method for adaptively compensating the damping anisotropy of hemispherical harmonic oscillators according to claim 1, wherein the motion equation is as follows:
3. the method for adaptively compensating for damping anisotropy in hemispherical harmonic oscillators according to claim 1, wherein the final auto-precession control f qs The calculation formula of (c) is:
wherein f is qs0 For initial self-precession control, f as For energy control, ω represents the average resonant frequency of the hemispherical harmonic oscillator.
4. A system for adaptively compensating the damping anisotropy of a hemispherical resonator, which is used for implementing a method for adaptively compensating the damping anisotropy of a hemispherical resonator as claimed in any one of claims 1 to 3, and which comprises: the device comprises a first obtaining module, a second obtaining module, a third obtaining module and a eliminating module;
the first obtaining module is used for obtaining a motion equation of the hemispherical harmonic oscillator;
the second obtaining module is used for applying energy control, orthogonal control, initial self-precession control and phase control to the hemispherical harmonic oscillator based on the motion equation to obtain a stable working state of the hemispherical harmonic oscillator;
the third obtaining module is used for performing partial differential operation on the energy control based on the stable working state, and overlapping the energy control with the initial automatic precession control to obtain final automatic precession control;
and the elimination module is used for eliminating the damping anisotropy of the hemispherical harmonic oscillator based on the final automatic precession control.
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